CN115499557A - Delay chaotic image encryption method based on Arnold mapping and multi-shift mapping function - Google Patents

Delay chaotic image encryption method based on Arnold mapping and multi-shift mapping function Download PDF

Info

Publication number
CN115499557A
CN115499557A CN202211114087.6A CN202211114087A CN115499557A CN 115499557 A CN115499557 A CN 115499557A CN 202211114087 A CN202211114087 A CN 202211114087A CN 115499557 A CN115499557 A CN 115499557A
Authority
CN
China
Prior art keywords
image
chaotic
sequence
mapping
arnold
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202211114087.6A
Other languages
Chinese (zh)
Other versions
CN115499557B (en
Inventor
赵朝锋
杜庆辉
尹承伟
翟志波
张永新
沈家全
李德光
赵鹏
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Luoyang Normal University
Original Assignee
Luoyang Normal University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Luoyang Normal University filed Critical Luoyang Normal University
Priority to CN202211114087.6A priority Critical patent/CN115499557B/en
Publication of CN115499557A publication Critical patent/CN115499557A/en
Application granted granted Critical
Publication of CN115499557B publication Critical patent/CN115499557B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
    • H04N1/44—Secrecy systems
    • H04N1/448—Rendering the image unintelligible, e.g. scrambling
    • H04N1/4486—Rendering the image unintelligible, e.g. scrambling using digital data encryption
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N7/00—Computing arrangements based on specific mathematical models
    • G06N7/08—Computing arrangements based on specific mathematical models using chaos models or non-linear system models
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T1/00—General purpose image data processing
    • G06T1/0021—Image watermarking
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/001—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using chaotic signals

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Signal Processing (AREA)
  • Evolutionary Computation (AREA)
  • Pure & Applied Mathematics (AREA)
  • Artificial Intelligence (AREA)
  • Computational Mathematics (AREA)
  • Data Mining & Analysis (AREA)
  • Nonlinear Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Algebra (AREA)
  • Computing Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Mathematical Physics (AREA)
  • Software Systems (AREA)
  • Computer Security & Cryptography (AREA)
  • Multimedia (AREA)
  • Image Processing (AREA)
  • Facsimile Transmission Control (AREA)

Abstract

The invention discloses a delayed chaotic image encryption method based on Arnold mapping and a multiple shift mapping function, which comprises the following steps: s1: selecting proper parameters and initial values as keys, generating a chaotic sequence by delaying and inducing a hyper-chaotic system, and carrying out imaging processing on the chaotic sequence to obtain an imaged sequence; s2: performing multi-round scrambling on the original image through Arnold mapping to obtain a scrambled image; s3: converting the scrambled image into a diffusion image through an imaging sequence; s4: and processing the diffusion image through an imaging sequence and a multi-shift mapping function to obtain a ciphertext image. The encryption method has an infinite-dimensional key space theoretically, and the sensitivity and the safety of the algorithm key are greatly improved. In addition, the encryption method has higher encryption speed and can effectively resist security attack. The encryption method solves the problems that the existing encryption method is too small in key space, poor in robustness, low in efficiency, difficult to resist plaintext attack and the like.

Description

Delay chaotic image encryption method based on Arnold mapping and multi-shift mapping function
Technical Field
The invention relates to the field of image information protection, in particular to a delayed chaotic image encryption method based on Arnold mapping and a multi-shift mapping function.
Background
Some digital images contain a lot of information and privacy, which are usually not desired to be illegally accessed and obtained by people, and thus, the protection of image information is a focus of attention. Meanwhile, personalized image protection technology is also concerned.
As is known, a digital image has the characteristics of large data size, high redundancy, strong correlation, and the like, and the conventional encryption method is not suitable for encrypting the digital image. The dynamic characteristics of chaos, such as sensitivity to initial values and parameters, unpredictability, pseudo-randomness, ergodicity and the like, are very suitable for encrypting digital images.
At present, as the demand for digital image protection increases, more personalized image information protection technologies are proposed. Although the chaotic image protection technology has remarkable advantages, the image encryption method based on the low-dimensional chaos has security defects, which is well known. The image encryption technology based on the high-dimensional chaos is questioned because the encryption process is simple and the key algorithm is too dependent on the security of the key stream. In addition, the chaotic image protection technology has various problems at present, such as the first element is irrelevant to the encryption and decryption algorithm; the nonlinear function is used as an encryption machine, so that the algorithm efficiency is low; the scrambling function is mostly periodic, and great potential safety hazard occurs; high dimensional chaos is difficult to realize.
Disclosure of Invention
In order to overcome the defects in the background art, the invention discloses a delayed chaotic image encryption method based on Arnold mapping and a multiple-shift mapping function, which aims to: the problems that the key space of the existing encryption method is too small, the robustness is poor, the efficiency is low, the first element is difficult to be related to the algorithm, the scrambling periodicity is difficult to be caused and the like are solved, the protection requirement of a user on image information is met, and the unique individual requirement of the user is also met.
In order to achieve the purpose, the invention adopts the following technical scheme:
a delayed chaotic image encryption method based on Arnold mapping and a multi-shift mapping function comprises the following steps:
s1: selecting proper parameters and initial values as keys, generating a chaotic sequence by delaying and inducing a hyper-chaotic system, and carrying out imaging processing on the chaotic sequence to obtain an imaged sequence;
s2: performing multi-round scrambling on the original image through Arnold mapping to obtain a scrambled image;
s3: converting the scrambled image into a diffusion image through an imaging sequence;
s4: and processing the diffusion image through an imaging sequence and a multi-shift mapping function to obtain a ciphertext image.
In the step 1, the hyper-chaotic system is a hyper-chaotic system with theoretical infinite dimensions, and the chaotic sequence generated by the hyper-chaotic system is a pseudo-random chaotic sequence.
Further improving the technical scheme, the S1 comprises the following steps:
s1.1: the mathematical model of the hyperchaotic system is as follows:
Figure BDA0003842318390000021
Figure BDA0003842318390000022
Figure BDA0003842318390000023
in the formula, a, b and c are parameters, x, y and z are state variables, k is linear feedback gain, and tau is delay time;
taking the last M X N values of the state sequences X, Y and Z to obtain three sequences X, Y and Z;
s1.2: converting the sequences X, Y and Z into sequences X ', Y ' and Z ' with the values of [0, 255] by the formula (2);
Figure BDA0003842318390000033
an imaging sequence Z is constructed by the formula (3) h Sequence of images Z h For obfuscating operations;
Z h ＝mod(X′+Y′，256)。 (3)
the method has the beneficial effects that the method is beneficial to carrying out deep fusion on the random sequence generated by the delayed chaos and the image, and achieves a potential encryption effect.
Further improving the technical scheme, in S2, the original image P is subjected to Arnold mapping by the formula (4) to obtain a scrambled image P 1 ；
Figure BDA0003842318390000031
In the formula, (i, j) is the pixel position of the original image P before transformation, (i ', j') is the pixel position of the original image P after transformation, a and b are transformation parameters, M is the length of the image, N is the width of the image, and mod (·) is modulo operation.
The method has the advantages that the periodicity of the scrambling function can be well avoided, and the scrambling effect of the algorithm is optimal.
Further improves the technical scheme, and sets a =113,b =97, the original image P is subjected to two rounds of Arnold mapping by equation (4), resulting in a scrambled image P 1 。
Further improving the technical scheme, the decryption mapping of the formula (4) is as follows:
Figure BDA0003842318390000032
further improving the technical scheme, the S3 comprises the following steps:
s3.1: will scramble the image P 1 Conversion to a one-dimensional pixel array P 2 Converting the complex structure of the image into a simpler one-dimensional structure;
s3.2: calculating an initial value P of the intermediate sequence by the formula (6) m (0) A random confusion mechanism is established, and the defect that the first element is irrelevant to the algorithm is overcome.
Figure BDA0003842318390000041
S3.3: generation of sequence P by formula (7) m (ii)；
P m (ii)＝mod(P 2 (ii)+P m (ii-1)+Z h (ii)，256) (7)
Wherein ii =1,2,3,4, \8230;, M × N.
The method has the advantages that the delayed chaotic system, the scrambling function, the linear function and the diffusion operation are combined, and a good encryption effect is achieved.
Further improving the technical scheme, the S4 comprises the following steps:
s4.1: reconstructing the segmentation function using a multiple shift mapping function;
Figure BDA0003842318390000042
wherein f is a linear piecewise function:
Figure BDA0003842318390000043
in the formula, C is a ciphertext image, p is a plaintext, k is a secret key, n is iteration times, and l is a parameter;
s4.2: will sequence P m And the sum sequence Z' is respectively used as a plaintext and a secret key of the formula (8) and the formula (9), and corresponding sequence value C is obtained after 2 times of iteration 1 ；
S4.3: c is to be 1 Reconstructing the matrix into an M multiplied by N matrix, then repeating the steps S1 to S3 to obtain a new round of reconstructed matrix, and finally forming a ciphertext image C.
The method has the advantages that the novel linear function is applied to the encryption machine, and the defect of low efficiency caused by the nonlinear function is overcome.
Due to the adoption of the technical scheme, compared with the background technology, the invention has the following beneficial effects:
the invention provides a delayed chaos image encryption method based on Arnold mapping and an improved multi-shift mapping function, which comprises the steps of firstly imaging a hyperchaotic sequence generated by delayed induction, and well fusing a random sequence generated by delayed chaos with an image depth; then, the original image is scrambled according to the characteristics of Arnold mapping, and the problem of periodic scrambling is solved. And then the problem that the first pixel in the plaintext is irrelevant to the algorithm is solved through diffusion operation. Finally, through the imaging sequence and the improved multi-shift mapping function, the linear function is well applied to the encryption machine, the confusion and diffusion effects are improved, and the algorithm efficiency is greatly improved.
When the encryption method adopts a hyperchaotic system generated by delay induction to encrypt the image, theoretically, a key space has infinite dimensions, and can resist various forms of statistical attacks. By utilizing the characteristics of Arnold mapping and an improved multi-shift mapping function and combining chaotic sequence imaging, the image achieves a good encryption effect and the encryption efficiency is improved. The execution of the diffusion operation establishes the relation between the first pixel of the image and the algorithm, and can effectively resist known or selected plaintext attacks.
The encryption method can provide larger key space, improves the sensitivity of the algorithm key, has higher encryption speed, and can effectively resist security attack. The encryption method solves the problems that the existing encryption method is too small in key space, poor in robustness, low in efficiency, difficult to correlate the first element with the algorithm, scrambling periodicity and the like.
The encryption method utilizes the delay phenomenon to generate a plurality of hyperchaotic attractors with different topological structures in a stable dynamic system, the hyperchaotic system shows more complex dynamic characteristics, and a brand new random generator source is provided for information security protection, and the thought is absolutely unique in the industry and is creative.
Drawings
Fig. 1 is a flowchart of a chaotic image encryption method with delay induced generation according to an embodiment of the present invention.
FIG. 2 is a diagram of a chaotic system with delay induced generation according to an embodiment of the present invention.
FIG. 3 is a "Cameraman" encryption-decryption graph and histogram of the encryption method in the embodiment of the present invention.
Fig. 4 is a key sensitivity test chart and histogram of the encryption method in the embodiment of the present invention.
Fig. 5 is a correlation distribution diagram of an encryption method in an embodiment of the present invention.
FIG. 6 is a test chart of an "all black" image of the encryption method in an embodiment of the present invention.
FIG. 7 is a test chart of an "all white" image of the encryption method in an embodiment of the present invention.
Fig. 8 is a line graph of "NPCR" of the encryption method in the embodiment of the present invention.
Fig. 9 is a line diagram of "UACI" of the encryption method in the embodiment of the present invention.
Fig. 10 is a diagram of the noise and shear attack resistance of the encryption method in the embodiment of the present invention.
FIG. 11 is a runtime share diagram for an encryption method in an embodiment of the invention.
Detailed Description
The following describes preferred embodiments of the present invention with reference to the drawings, and explains effects of the implementation of the encryption method. It should be understood by those skilled in the art that these embodiments are only for explaining the technical principle of the present invention, and are not intended to limit the scope of the present invention.
Referring to fig. 1, a delayed chaotic image encryption method based on Arnold mapping and a multiple shift mapping function includes the following steps:
s1: selecting proper parameters and initial values as keys, generating a pseudo-random chaotic sequence by delaying and inducing the hyper-chaotic system, and carrying out imaging processing on the pseudo-random chaotic sequence to obtain an imaged sequence.
The hyper-chaotic system has theoretical infinite dimensionality, appropriate parameters and initial values are selected as keys, the hyper-chaotic system generated by delaying induction can generate a chaotic attractor with the theoretical infinite dimensionality as shown in figure 2, and the chaotic attractor shows that the generation mechanism of the chaotic system is simple and feasible, has more complex dynamic characteristics, and has better potential to be applied to the field of information safety. The pseudo-random chaotic sequence of the chaotic attractor is subjected to imaging processing, so that the sequences X ', Y ', Z ' and the imaging sequence Zh can be obtained, and the depth fusion of the chaotic system and the image in the encryption method is shown. The encryption method can effectively expand the key space, achieve infinite dimension in theory and effectively resist the attack of statistics.
Specifically, S1 comprises the following substeps:
s1.1: taking the Chen system as an example, the mathematical model of the hyperchaotic system is as follows:
Figure BDA0003842318390000071
Figure BDA0003842318390000072
Figure BDA0003842318390000073
(1) In the formula, a, b and c are parameters, x, y and z are state variables, k is linear feedback gain, and tau is delay time. When k =0, the system is stable.
As shown in fig. 2 (a), when a =35, b =3, c =18.5, and k =0, the hyper-chaotic system is a normal stable Chen system (without delay characteristics). Starting from a certain initial condition, one of two stable equilibrium points is converged.
As shown in fig. 2 (b), when a =35, b =3, c =18.5, k =3.8 and τ =0.3, the hyper-chaotic system has a delay characteristic, and hyper-chaos is generated, and a compound multi-scroll hyper-chaotic attractor is presented.
As shown in fig. 2 (c), when a =35, b =3, c =18.5, k =2.85 and τ =0.3, the hyper-chaotic system is still hyper-chaotic and presents a double-scroll hyper-chaotic attractor.
As shown in fig. 2 (d), when a =35, b =3, c =18.35978, k =2.85 and τ =0.3, the system is still hyper-chaotic and presents a single scroll hyper-chaotic attractor.
Determining parameters a =35, b =3, c =18.5, k =3.8, τ =0.3 of the delay-induced hyper-chaotic system, initial values x (0) =0.1, y (0) =0.1, z (0) =0.1, and initial conditions on [ - τ, 0) are: z (t) =0, - τ ≦ t < 0. To avoid transient effects, the values of the delayed attractor system (1) evolution over 0 < t < Tp (Tp =50 in the present invention) are not used. And (3) generating state sequences X, Y and Z with the length of M X N by system evolution to form three sequences X, Y and Z.
S1.2: the imaging operation is carried out by the formulas (2) and (3), and the sequences X, Y and Z are converted into values of [0, 255]]To obtain an imaged sequence Z h 。
Figure BDA0003842318390000082
An imaging sequence Z is constructed by the formula (3) h Of an imaging sequence Z h For obfuscating operations.
Z h ＝mod(X′+Y′，256)。 (3)
The method has the advantages that the method is favorable for carrying out depth fusion on the random sequence generated by the delayed chaos and the image, and achieves a potential encryption effect.
S2: and performing multi-round scrambling on the original image through Arnold mapping to obtain a scrambled image.
Specifically, in S2, assuming that a =113 and b =97, two rounds of Arnold mapping are performed on the original image P by equation (4), and the scrambled image P is obtained 1 。
Figure BDA0003842318390000081
Where (i, j) is the pixel position of the original image P before transformation, (i ', j') is the pixel position of the original image P after transformation, a and b are transformation parameters, M is the length of the image, N is the width of the image, and mod (·) is a modulo operation.
The method has the advantages that the periodicity of the scrambling function can be well avoided, and the scrambling effect of the algorithm is optimal.
The inverse transform of the Arnold mapping is a decrypted mapping, which is:
Figure BDA0003842318390000091
s3: converting the scrambled image into a diffused image through an imaging sequence;
specifically, S3 includes the following substeps:
s3.1: will scramble the image P 1 Conversion to a one-dimensional pixel array P 2 ；
S3.2: calculating an initial value P of the intermediate sequence by the formula (6) m (0)；
Figure BDA0003842318390000092
S3.3: generation of sequence P by formula (7) m (ii)；
P m (ii)＝mod(P 2 (ii)+P m (ii-1)+Z h (ii)，256) (7)
Wherein ii =1,2,3,4, \ 8230;, M × N.
The method has the advantages that the scrambled image is converted into the diffused image, and the relation between the first element and the algorithm is established, so that the attack of selection or known plaintext can be well resisted. In addition, the delayed chaotic system, the scrambling function, the linear function and the diffusion operation are combined, so that a good encryption effect is achieved.
S4: the diffusion image is processed through the imaging sequence and the multi-shift mapping function, the linear function is applied to the encryption machine, the encryption efficiency is effectively improved, and the ciphertext image is quickly obtained. In particular, according to the sequence Z' and P of the imaging m And substituting the modified multi-shift mapping function as a corresponding plaintext and a corresponding key to obtain a final ciphertext image.
S4, the method comprises the following steps:
s4.1: reconstructing the segmentation function using a multiple shift mapping function;
Figure BDA0003842318390000101
wherein f is a linear piecewise function:
Figure BDA0003842318390000102
in the formula, C is a ciphertext image, p is a plaintext, k is a secret key, n is iteration times, and l is a parameter;
in the present embodiment, l =128,n =2.
S4.2: will sequence P m And the sequence Z' is respectively used as a plaintext and a secret key of the formula (8) and the formula (9), and corresponding sequence value C is obtained after 2 iterations 1 ；
S4.3: c is to be 1 Reconstructing the matrix into an M multiplied by N matrix, then repeating the steps S1 to S3 to obtain a new round of reconstructed matrix, and finally forming a ciphertext image C.
The method has the advantages that the novel linear function is applied to the encryption machine, and the defect of low efficiency caused by the nonlinear function is overcome.
The following are the performance tests and analyses of the encryption method, which can well verify the advantages of the encryption method, and the performance tests and analyses comprise the following parts:
(1) analyzing encryption and decryption effects;
(2) analyzing a key space;
(3) analyzing the sensitivity of the key;
(4) analyzing the correlation;
(5) information entropy analysis;
(6) analyzing against known or chosen plaintext attacks;
(7) analyzing the resistance to differential attack;
(8) data loss and noise analysis resistance;
(9) and analyzing the operation efficiency.
To illustrate the universality of the invention, test images are all selected from a USC-SIPI image library, a computer is configured as AMD Ryzen 53550H CPU and 8GB RAM, and corresponding tests are carried out on a platform of MATLAB2016 a.
(1) And (3) encryption and decryption effect analysis:
as shown in fig. 3, a "Cameraman" graph (256 × 256) is selected for the encryption and decryption tests, and the original image, the encrypted image, and the decrypted image and their corresponding histograms are shown in fig. 3. The encrypted image has small average fluctuation of the histogram as a noise image, which means that the encryption method of the present invention can effectively resist statistical attack in the pixel value distribution sense.
(2) And (3) key space analysis:
if only 5 parameters (a, b, c, k, tau) and three initial values (x (0), y (0), z (0)) of the hyper-chaotic system generated by delay induction are used as keys, the formed key space is 2 256 (calculation accuracy 2 -32 ). If the hyperchaotic system generated by delay induction is in [ -tau, 0 []The above initial condition also acts as a key, the key space will expand to a theoretically infinite dimension. Therefore, the key space of the image encryption method of the present invention canResisting any brute force attack.
(3) Key sensitivity analysis:
fig. 4 shows the results of the key sensitivity analysis. 4 (a) and (d) are histograms of the original image and its corresponding image, 4 (b) and (e) are histograms of the decrypted image and its image using the correct key (z (0) =0.1, other key values are unchanged), and 4 (c) and (f) are histograms of the decrypted image and its image using the slightly different key (z (0) =0.1+ 10) -14 Other key values are not changed) of the same encrypted image and its corresponding histogram. As can be seen from fig. 4, the original image can only be reconstructed from the encrypted image with the correct key, even a slightly different key will result in a completely different decrypted image. This illustrates that the image encryption method of the present invention is very sensitive to the key in the encryption and decryption processes.
(4) And (3) correlation analysis:
fig. 5 shows the correlation of the original image "Cameraman" (256 × 256) and the corresponding encrypted image in the horizontal direction, the vertical direction, and the diagonal direction. In addition, table 1 shows the quantitative results of the image neighboring pixel correlation test. This also shows that statistical attacks on the image encryption method of the present invention do not allow attackers to obtain any valuable information.
TABLE 1 neighboring Pixel correlation analysis of original image and encrypted image
Figure BDA0003842318390000121
Figure BDA0003842318390000131
(5) Information entropy analysis:
table 2 shows the information entropy values of the original image and the corresponding encrypted image, which indicates that the information leakage rate of the image encryption method of the present invention is close to zero, which means a higher degree of randomness in the sense of information entropy.
Table 2 entropy of information of encrypted image
Figure BDA0003842318390000132
(6) Analysis against known or selected plaintext attacks
An adversary would select some special original image, such as a full black image or a full white image (256 × 256), and obtain the corresponding encrypted image to deduce the key or reveal the relationship between the original image and the ciphertext image. In the confusion stage of the image encryption method, the confusion value is related to the scrambled image, and a multi-shift mapping function is added, so that the relationship between a ciphertext and a plaintext is more complex. Therefore, the image encryption method can effectively resist known or selected plaintext attacks. As shown in fig. 6 and 7, the encryption results of the all-black and all-white images are similar to noise, and have a good encryption effect.
(7) And (3) carrying out differential attack resisting analysis:
tables 3 and 4 give the NPCR and UACI values for the encrypted images, and figures 9 and 10 give the NPCR and UACI value line graphs. It can be seen that the NPCR and UACI values for the encryption method of the present invention are close to the expected values of 99.6094% and 33.4635%. In fig. 9 and 10, the polyline of the encryption method of the present invention and the expected value polyline are almost overlapped at the key point, which shows that the encryption method of the present invention is quite stable against differential attacks and does not change drastically with the change of the image.
TABLE 3 test results of NPCR (%)
Figure BDA0003842318390000141
TABLE 4 test results (%)
Figure BDA0003842318390000142
(8) Data loss and noise resistance analysis:
fig. 10 shows the result of using the image encryption method of the present invention to resist noise attack and partial data loss in an image. As can be seen from fig. 10, although the encrypted image suffers from different types of noise pollution or data loss of different sizes, the recognizable original image can still be recovered after decryption by using the image encryption method of the present invention, which shows that the image encryption method of the present invention has good robustness.
(9) Analyzing the operation efficiency:
table 5 lists the average encryption times for 30 monte carlo tests using different images. The tests were performed in the MATLAB environment of a computer (AMD) Ryzen 53550H CPU and 8gb RAM). Fig. 11 shows the time share of the whole encryption process, the chaotic evolution time (HCMACS-TD) accounts for 29% of the total time, the Arnold mapping process accounts for 16% of the total time, the diffusion process accounts for 14% of the total time, and the multiple shift mapping function process accounts for about 41% of the total time.
TABLE 5 average running time(s) of the algorithm
Figure BDA0003842318390000151
The foregoing has described the basic principles and principal features of the invention. When the image encryption method adopts a hyperchaotic system generated by delaying induction to encrypt the image, theoretically, a key space has infinite dimensions. By utilizing the characteristics of Arnold mapping and an improved multi-shift mapping function and combining the imaging of the chaotic sequence, the image achieves a good encryption effect. The execution of the diffusion operation establishes the relation between the first pixel of the image and the ciphertext, and can more effectively resist known or selected plaintext attacks.
The method can provide larger key space, improve the sensitivity of the algorithm key, has higher encryption speed and is more suitable for image information security protection.
The encryption method solves the problems that the existing encryption method is too small in key space, poor in robustness, low in efficiency, difficult to resist plaintext or select plaintext to attack and the like.
The details of which are not described in detail in the prior art. Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (8)

1. A delayed chaotic image encryption method based on Arnold mapping and multiple shift mapping functions is characterized in that: the method comprises the following steps:
s1: selecting proper parameters and initial values as keys, generating a chaotic sequence by delaying and inducing a hyper-chaotic system, and carrying out imaging processing on the chaotic sequence to obtain an imaged sequence;
s2: performing multi-round scrambling on the original image through Arnold mapping to obtain a scrambled image;
s3: converting the scrambled image into a diffused image through an imaging sequence;
s4: and processing the diffusion image through an imaging sequence and a multi-shift mapping function to obtain a ciphertext image.
2. The method for encrypting the delayed chaotic image based on the Arnold mapping and the multiple shift mapping function as claimed in claim 1, wherein: in S1, the hyper-chaotic system is a hyper-chaotic system with theoretical infinite dimensions, and a chaotic sequence generated by the hyper-chaotic system is a pseudo-random chaotic sequence.
3. The method for encrypting the delayed chaotic image based on the Arnold mapping and the multiple shift mapping function as claimed in claim 1, wherein: s1 comprises the following sub-steps:
s1.1: the mathematical model of the hyperchaotic system is as follows:
Figure FDA0003842318380000011
Figure FDA0003842318380000012
Figure FDA0003842318380000013
in the formula, a, b and c are parameters, x, y and z are state variables, k is linear feedback gain, and tau is delay time;
taking the last M X N values of the state sequences X, Y and Z to form three sequences X, Y and Z;
s1.2: converting the sequences X, Y and Z into sequences X ', Y ' and Z ' with the values of [0, 255] through the formula (2);
Figure FDA0003842318380000023
an imaging sequence Z is constructed by the formula (3) h Of an imaging sequence Z h For obfuscating operations;
Z h ＝mod(X′+Y′，256)。 (3)
4. the method for encrypting the delayed chaotic image based on the Arnold mapping and the multiple shift mapping function as claimed in claim 3, wherein: in S2, arnold mapping is carried out on the original image P through the formula (4) to obtain a scrambled image P 1 ；
Figure FDA0003842318380000021
Where (i, j) is the pixel position of the original image P before transformation, (i ', j') is the pixel position of the transformed image, a and b are transformation parameters, M is the length of the image, N is the width of the image, and mod (·) is the modulo operation.
5. The method for encrypting the delayed chaotic image based on the Arnold mapping and the multiple shift mapping function as claimed in claim 4, wherein: let a =113,b =97, by the formula (a =113, b = 97)4) Performing two rounds of Arnold mapping on the original image P to obtain a scrambled image P 1 。
6. The method for encrypting the delayed chaotic image based on the Arnold mapping and the multiple shift mapping function as claimed in claim 4 or 5, wherein: the decryption mapping of equation (4) is:
Figure FDA0003842318380000022
7. the method for encrypting the delayed chaotic image based on the Arnold mapping and the multiple shift mapping function as claimed in claim 4, wherein: s3, the method comprises the following steps:
s3.1: will scramble the image P 1 Conversion to a one-dimensional pixel array P 2 ；
S3.2: calculating the initial value P of the intermediate sequence by the formula (6) m (0)；
Figure FDA0003842318380000031
S3.3: generation of sequence P by formula (7) m (ii)；
P m (ii)＝mod(P 2 (ii)+P m (ii-1)+Z h (ii)，256) (7)
Wherein ii =1,2,3,4, \ 8230;, M × N.
8. The method for encrypting the delayed chaotic image based on the Arnold mapping and the multiple shift mapping function as claimed in claim 7, wherein: s4, the method comprises the following steps:
s4.1: reconstructing the segmentation function using a multiple shift mapping function;
Figure FDA0003842318380000032
wherein f is a linear piecewise function:
Figure FDA0003842318380000033
in the formula, C is a ciphertext image, p is a plaintext, k is a secret key, n is iteration times, and 1 is a parameter;
s4.2: will sequence P m And the sequence Z' is respectively used as a plaintext and a secret key of the formula (8) and the formula (9), and corresponding sequence value C is obtained after 2 iterations 1 ；
S4.3: c is to be 1 Reconstructing the matrix into an M multiplied by N matrix, then repeating the steps S1 to S3 to obtain a new round of reconstructed matrix, and finally forming a ciphertext image C.
CN202211114087.6A 2022-09-13 2022-09-13 Arnold mapping and multi-shift mapping function-based delayed chaotic image encryption method Active CN115499557B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202211114087.6A CN115499557B (en) 2022-09-13 2022-09-13 Arnold mapping and multi-shift mapping function-based delayed chaotic image encryption method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202211114087.6A CN115499557B (en) 2022-09-13 2022-09-13 Arnold mapping and multi-shift mapping function-based delayed chaotic image encryption method

Publications (2)

Publication Number Publication Date
CN115499557A true CN115499557A (en) 2022-12-20
CN115499557B CN115499557B (en) 2023-07-21

Family

ID=84469330

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202211114087.6A Active CN115499557B (en) 2022-09-13 2022-09-13 Arnold mapping and multi-shift mapping function-based delayed chaotic image encryption method

Country Status (1)

Country Link
CN (1) CN115499557B (en)

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106570814A (en) * 2016-10-17 2017-04-19 广东工业大学 Novel hyper-chaotic image encryption method
CN110245501A (en) * 2019-05-10 2019-09-17 西安理工大学 A kind of image encryption method based on infinite dimension ultra-chaos
CN111190049A (en) * 2020-01-14 2020-05-22 洛阳师范学院 Method for detecting nano-volt level weak sinusoidal signal by chaotic system of principal component analysis
CN112084517A (en) * 2020-09-15 2020-12-15 郑州轻工业大学 Image encryption method based on chaotic mapping and bit-level permutation
CN112800444A (en) * 2021-01-19 2021-05-14 桂林电子科技大学 Color image encryption method based on two-dimensional chaotic mapping
DE202022102430U1 (en) * 2022-05-04 2022-05-17 Rama Prasath Alagarswamy An optimized 2D chaotic mapping system for image security using an improved Sealion optimization algorithm
CN114915400A (en) * 2022-05-11 2022-08-16 集美大学 Synchronous time adjustable heterogeneous fractional order hyperchaotic system image encryption and decryption method

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106570814A (en) * 2016-10-17 2017-04-19 广东工业大学 Novel hyper-chaotic image encryption method
CN110245501A (en) * 2019-05-10 2019-09-17 西安理工大学 A kind of image encryption method based on infinite dimension ultra-chaos
CN111190049A (en) * 2020-01-14 2020-05-22 洛阳师范学院 Method for detecting nano-volt level weak sinusoidal signal by chaotic system of principal component analysis
CN112084517A (en) * 2020-09-15 2020-12-15 郑州轻工业大学 Image encryption method based on chaotic mapping and bit-level permutation
CN112800444A (en) * 2021-01-19 2021-05-14 桂林电子科技大学 Color image encryption method based on two-dimensional chaotic mapping
DE202022102430U1 (en) * 2022-05-04 2022-05-17 Rama Prasath Alagarswamy An optimized 2D chaotic mapping system for image security using an improved Sealion optimization algorithm
CN114915400A (en) * 2022-05-11 2022-08-16 集美大学 Synchronous time adjustable heterogeneous fractional order hyperchaotic system image encryption and decryption method

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
赵朝锋: "基于延迟超混沌的信息安全增强方法研究", 中国博士学位论文全文数据库信息科技辑, pages 138 - 26 *
郑海彭: "Arnold变换详解", pages 1 - 4, Retrieved from the Internet <URL:https://www.jianshu.com/p/39727/dbaffd9> *
闫丽宏 等: "基于Sprott-O混沌映射与Arnold变换的图像加解密算法", 河南科学, vol. 33, no. 10, pages 1696 - 1700 *

Also Published As

Publication number Publication date
CN115499557B (en) 2023-07-21

Similar Documents

Publication Publication Date Title
Norouzi et al. A novel image encryption based on hash function with only two-round diffusion process
Iqbal et al. Dynamic 3D scrambled image based RGB image encryption scheme using hyperchaotic system and DNA encoding
CN108898025A (en) New chaotic image encryption method based on dual scramble and DNA encoding
CN109889686B (en) Image encryption method based on H fractal structure and dynamic self-reversible matrix
CN107094072B (en) Mixed chaotic encryption method based on generalized Henon mapping
Wang et al. Pixel-level and bit-level image encryption method based on Logistic-Chebyshev dynamic coupled map lattices
Jun et al. A new image encryption algorithm based on single S-box and dynamic encryption step
Shahna et al. Novel hyper chaotic color image encryption based on pixel and bit level scrambling with diffusion
CN107330338B (en) Color image encryption and decryption method and system based on double-chaos cross diffusion
Fu et al. A symmetric image encryption scheme using chaotic baker map and Lorenz system
Liu et al. Cryptanalysis and enhancement of an image encryption scheme based on bit-plane extraction and multiple chaotic maps
CN110572252A (en) image encryption and decryption method based on fractional order translation chaotic system
Ye A novel image encryption scheme based on generalized multi-sawtooth maps
CN104050617A (en) Method for image encryption based on Liu chaotic system
Zhang et al. A fast piecewise image encryption scheme combining NC1DNSM and P-Box
Ramadan et al. Permutation-substitution image encryption scheme based on a modified chaotic map in transform domain
Aboughalia et al. Color image encryption based on chaotic block permutation and XOR operation
CN114401351A (en) Image encryption and decryption method based on novel two-dimensional fractional order chaotic mapping
CN111444522B (en) Random blocking chaotic image encryption method
Li et al. An image encryption method based on tent and Lorenz chaotic systems
Mohamed et al. Hybrid DCT-DWT watermarking and IDEA encryption of internet contents
Chapaneri et al. Chaos based image encryption using latin rectangle scrambling
CN116192362A (en) Lyapunov exponent adjustable chaotic system and image encryption and decryption method
CN115499557A (en) Delay chaotic image encryption method based on Arnold mapping and multi-shift mapping function
Khan et al. A New Multi Chaos-Based Compression Sensing Image Encryption.

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant